EARTH SCIENCE LAB
Impact Craters

Purpose

The purpose of this activity is to determine the impact velocity of different free falling objects, to calculate the resulting impact crater diameter, and to describe the features associated with impact craters.

Procedure

In this experiment the ball bearings will be the free falling objects which will simulate a meteorite or asteroid impact. Any object which is allowed to free fall in the Earth's gravitational field will experience an acceleration (g) equal to 9.8 m/s2. In order to determine the velocity of the ball bearing at the moment of impact, two equations are needed. The equation,

(1) vf = vi- gt

states that the final velocity, vf, is equal to the initial velocity, vi, minus the acceleration due to gravity, g, multiplied by the amount of time, t, it takes the object to fall. During this experiment you will be unable to accurately measure the fall time. Because of this, another equation is needed to determine the final velocity.

(2) d = vit - 0.5gt2

Equation (2) allows you to calculate the distance, d, an object will fall within the Earth's gravitational field, if the amount of fall time is known. It should be noted that d is negative (-) for objects moving towards the Earth. In other words a falling object has a negative displacement. For objects moving away from the Earth, d will be positive (+). Notice that time, t, is still a part of equation (2). By substitution, we can eliminate t and can then calculate vf based solely on the distance the object falls.

The initial velocity in these experiments is equal to zero, since the ball bearing is not moving prior to being released. This then simplifies the equations (1) and (2) to:

(3) vf = -gt

(4) d = -0.5gt2

By manipulation of equation (3) we get

(5) t = -vf /g

Substituting equation (5) into equation (4) results in the following:

(6) d = -0.5g(-vf /g)2

Simplification of equation (6) results in:

(7) vf 2 = -(2dg)

(8) vf  = (-2dg)0.5

By using equation (8), if you know the distance the free falling object has moved, you can calculate its impact velocity. Velocity is measured in meters per second.

To calculate the amount of energy released during the impact, the following equation is used:

(9) E = mv2

E is the energy release in joules (J), m is the mass of the falling object in kilograms and v is the impact velocity in meters per second. For example, if a 10 kg meteorite hit the Earth with an impact velocity of 10 m/s, the energy released would be:

(10)  E = 10kg(10m/s)2 = 1000J

In 2007, Vanissra Boonyaleepun and Se-Won Jang determined a mathematical relationship between the energy released from a ball dropped into a sand pit and the diameter of the resulting impact crater. D is the diameter in meters of the resulting crater, and E is the energy released in Joules.

(11)  D = (0.098 m/J) x E0.17

Crater Width

The crater width is measured across the bowl or depression of the crater from rim crest to rim crest.

Diagram showing how to measure crater width and ejecta width.

Impact Calculations

Column A: Using equation (8), complete the calculations to determine the final impact velocity (vf ) of a ball bearing dropped into a sand pit.
Report all values to 2 decimal places; Example 0.23, 1.34

Column B: Using equation (9), complete the calculations to determine the energy released (E) by a ball bearing dropped into a sand pit.
Report all values to 3 decimal places; Example 0.232, 1.348

Column C: Using equation (11), complete the calculations to determine the diameter (D) of the crater created by a ball bearing dropped into a sand pit.
Report all values to 3 decimal places; Example 0.232, 1.348

  A B C
Impact Ball Bearing
Mass (kg)		 Height,
d (meters)		 Initial Velocity,
vi (m/s)		 Impact Velocity,
vf (m/s)		 Energy Released
(Joules)		 Crater Width
(meters)
1 0.00353 kg 0.5 m 0 m/s m/s J m
2 0.00353 kg 1.25 m 0 m/s m/s J m
3 0.00353 kg 3 m 0 m/s m/s J m
4 0.00353 kg 5 m 0 m/s m/s J m
5 0.00353 kg 10 m 0 m/s m/s J m
6 0.01634 kg 0.5 m 0 m/s m/s J m
7 0.01634 kg 1.25 m 0 m/s m/s J m
8 0.01634 kg 3 m 0 m/s m/s J m
9 0.01634 kg 5 m 0 m/s m/s J m
10 0.01634 kg 10 m 0 m/s m/s J m

, Birkeland, Thomson and the craters labeled A, B and C. Do all of the craters have the same appearance? Explain any differences seen.

Descriptions of Existing Impact Craters

Examine the image of the Moon shown below. Describe the appearance of the following craters;

De Vries Crater description:

Crater "C" description:


De Vries Crater Region, Lunar farside
De Vries Crater on the lunar farside. Its diameter is approximately 59 kilometers. (Image courtesy of NASA)

Looking at Craters A, B and C, which crater is the oldest and which is the youngest?

               Youngest:
               Middle:
               Oldest:
                            

What is the main erosive process on the surface of the Moon? Remember there is no atmosphere on the Moon.